The Scottish First Minister said the legislation actually removing the UK from the EU would likely require "legislative consent" of the devolved assemblies, including Scotland's parliament where nearly half the MSPs are Sturgeon's SNP.
Leave won Thursday's referendum 52% to 48% but 62% of Scots who turned out voted to remain.
Chaos is currently reigning in Westminster, with confusion over when Britain will actually commence the process of leaving the EU, as set out by the Treaty of Lisbon, and both main parties in chaos after David Cameron resigned and Jeremy Corbyn potentially about to face a leadership challenge.
Having previously suggested she would call a second independence referendum to keep Scotland in the EU, Sturgeon told The BBC's Sunday Politics Show: "The issue you are talking about is would there have to be a legislative consent motion or motions for the legislation that extricates the UK from the European Union?
"Looking at it from a logical perspective, I find it hard to believe that there wouldn't be that requirement - I suspect that the UK government will take a very different view on that and we'll have to see where that discussion ends up."
She added: "If the Scottish Parliament was judging this on the basis of what's right for Scotland then the option of saying look we're not to vote for something that's against Scotland's interest, of course that's got to be on the table."
The call for a second independence referendum won the endorsement of The Daily Record, an influential Scottish paper.
Sturgeon has said a referendum is "on the table".